In 1934, Edward A. Doisy of Washington University extracted 3000 ...

Question

In 1934, Edward A. Doisy of Washington University extracted 3000 lb of hog ovaries to isolate a few milligrams of pure estradiol, a potent female hormone. Doisy burned 5.00 mg of this precious sample in oxygen and found that 14.54 mg of CO2 and 3.97 mg of H2O were generated.

b. The molecular weight of estradiol was later determined to be 272. Determine the molecular formula of estradiol

Accepted Answer

Hey everyone, let's tackle this problem. It says a scientist was able to isolate a few milligrams of pure testosterone, a primary sex hormone in males when the scientists burned mg of the testosterone. He had, sorry, five mg of the testosterone sample he had isolated in oxygen. He found that 14.496 mg of C. 02 and 4.373 mg of H 20. Were generated in the chemical reaction, determine the molecular formula of testosterone. If the molecular weight analysis showed that the molecular weight of testosterone is 288 g per mole. Alright, so where do we start with this? Well, I like to look at what I'm given and where I'm trying to go. What's the final thing that I'm going to solve for in this problem? So let's sort of look at those two and then connect the dots in the middle. So they give me a reaction where we burn testosterone in oxygen to form C. 02 and H 20. That sounds like a familiar reaction. Right, yep, that's combustion. So I'm going to write just a little formula to represent this reaction and we can write that as T for testosterone plus, oxygen yields C. +02 and H +20. Okay, so that's what we were given and we were given the amounts of testosterone. So we're given the amounts of testosterone C. +02 and H +20. Okay, and we're looking for the molecular formula. Right, We have our molecular formulas here. So how can I get from what's given to the molecular formula? Well, we know that the molecular formula has the number of moles or the molar ratio? The molar ratio of each element in the compound. So how can we get the molar ratio by finding out the number of moles of each element in the compound? So that would be carbon, hydrogen and oxygen in this case. Right. In testosterone. Okay, well, how do I find out the number of moles of carbon, hydrogen oxygen in testosterone? Hm Well, I was given the amount of carbon dioxide and hydrogen, Or sorry, water produced from the original amount of testosterone. Hmm Well, Let's write that out. So what can we find from 14.496 mg of c. 0 2. Well, notice that there's no other carbon in this reaction. So all of our carbon produced, yes, all of our carbon produced in C. 02 in this reaction must come from all of that testosterone, the carbon and testosterone. So I can use stoke geometry to convert this amount of carbon dioxide to the amount of carbon are in milligrams in this case. So milligrams of carbon in testosterone and I can do the same with the water. So I can convert that 4.37 hoops, 4.373 mg of water to find the milligrams of hydrogen and testosterone. Right, Because similar to carbon, there's no other hydrogen in the reaction. So it all must be coming from that testosterone. Okay, now, what about the oxygen? So I see that we're burning oxygen but we can assume that there's also oxygen and testosterone. Looking at the answer choices and there's no other, no other elements like nitrogen or anything in here. Well, if I have the milligrams of carbon, the milligrams of hydrogen, milligrams of carbon, milligrams of hydrogen and I want the milligrams of oxygen, I have the milligrams of testosterone. So I can solve for those milligrams of oxygen. Right, okay, well then once I have all the milligrams of each element, can I convert that to the moles of each element? Like I need a number three. So once we have those milligrams we will convert the milligrams to. Well in this case we're gonna use mila moles just because we're using milligrams. So we usually use grams to moles. So now we're using milligrams. So we'll use mila moles just for simplicity. Okay, so then once we convert to our mila moles, we'll get our molar ratio. So that fills in the gaps between the beginning and the end of this, the steps for this problem. Okay, I hope that showed the thought process of how I got from what they're giving me and where I need to go and figuring out the steps in between. Okay, so let's apply these steps to our problem and tackle this? So like I said in the first step, we're converting our amount of products to isolating that element in testosterone. So let's start with carbon. And if you're feeling uneasy about stoic geometry, definitely go back and watch some videos of how to do unit conversions. So we bring that unit down to the bottom and we have milligrams of C. 02 and we can convert that to moles or mila moles of C rather. So in one mil a mole of C 02, we have 44.1 mg of SEO to write the molar mass of C 02. And we're trying to get two mg of carbon. Well I can do my molar ratio here. So in one mil a mole of C. O. To carry that unit down diagonally. Then I have how many moles of carbon in there also? one right, 1 Mole of carbon per mole of CO two. Now I have mole or mila mole of carbon. And can I convert that to milligrams of carbon? Yes, with the Molar mass which is 12.01. Alright, if you multiply that altogether cancel out the units, you get 3.956 mg of carbon. And that's in our testosterone. Right. Our original amount of testosterone. Cool, good job, let's do the same thing for our high hydrogen in H 20. So we're starting with 4.373. Always starting with what is given, Making sure our units cancel out. So we can drag that milligrams of H20 down here and we have 18.16 mg of H 20 and one mil a mole of H 20. Now, same same thing as CO2. We're going to convert that H 20 with our molar ratio to hydrogen, but this time it's to mila moles, right? Two atoms of H 202 moles of H and one H 20 molecule, one mole of H 20, I should say. And now we have one mil a mole of H 20. Can convert to 1.008 mg of hydrogen. I'm sorry, that's minimal of oops, I messed up my units here. That's two million moles of hydrogen and one minimal of hydrogen. Right? We're doing that molar ratio And this equals .489 Milligrams of hydrogen. And that's again in our original amount of testosterone, right, because it's all coming from testosterone cool. So we finished step one Now, step two. Remember we have our original amount of carbon are original amount of hydrogen. We know the final amount of testosterone. So we can use those values to solve for our amount of oxygen with some simple algebra. Okay, so let's do that. five mg of testosterone equals 3.956 mg of carbon plus 0.489 mg of hydrogen plus, let's say X milligrams of oxygen. You subtract the carbon and hydrogen values to the other side and you will get that X equals .555 mg of oxygen. Well, yes, and I'll look angel numbers. That must be a good sign. You guys are gonna do great on your next test. Um great. So now we have our initial amounts for all of our elements in testosterone. So remember in our molecular formula we're looking for the number of moles in each of each element in testosterone because the amount is fixed, right? We are figured out these amounts in testosterone that are fixed. So the molar ratio will also be fixed if we convert them to moles and we can figure out our molecular formula by making them into whole numbers. So step three, we're converting Milligrams, two mila moles to find our moller molecular formula. Okay, so we want our ratio of carbon to hydrogen to oxygen. So we're going to have to switch colors here. How much carbon? So we have 3.956 mg of carbon. And we're just dividing by the molar mass because it's in per one mole. Right? So 12.011 mg of carbon. And for hydrogen we have . mg of hydrogen. The Mueller mass is 1.0082 mg of hydrogen I guess I should say per per mil Immel because that will cancel out the units. Ah this is corbin, Okay, per million hydrogen. And our last one is .555 Milligrams of oxygen divided by milligrams per mil Immel oxygen. Okay, so if you do that math, you will get . .4851 for hydrogen and 0.3469 moles four oxygen. Can I write these as my subscription? My molecular formula. No, that would be ugly. So, we want whole numbers. So we're gonna divide all by the smallest number. Okay, so we're gonna divide all of these by .03469. Okay, by each number. And that will give us 9. 14 and one AM I happy or these whole numbers? No, but I see that this is .5 a half. So if I multiply all of these by two, then I will finally get my whole numbers. So if I do that, we get 19 28 2. So if I write that in my molecular formula, it would be C 19 H 28 02. And that will be my molecular formula, which is answer choice c. Okay. And the problem says that my molecular weight of testosterone is 2 88 g per mole. So if you wanted to confirm the molecular weight you can multiply 19 times the molar mass of carbon 28 times more massive hydrogen. Two times the molar mass of oxygen, add them all up. And it confirms that the Mueller or sorry, the molecular weight is 288. Which tells you that we did this problem, correct? I hope this video is helpful, and thanks for watching.

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